Find the Standard Form of the Parabola f(x)=4(x-2)^2+4

$f (x) = 4 {(x - 2)}^{2} + 4$

Step 1

Write $f (x) = 4 {(x - 2)}^{2} + 4$ as an equation.

$y = 4 {(x - 2)}^{2} + 4$

Step 2

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 {(x - 2)}^{2} + 4 = y$

Step 3

Subtract $4$ from both sides of the equation.

$4 {(x - 2)}^{2} = y - 4$

Step 4

Divide each term in $4 {(x - 2)}^{2} = y - 4$ by $4$ and simplify.

Divide each term in $4 {(x - 2)}^{2} = y - 4$ by $4$ .

$\frac{4 {(x - 2)}^{2}}{4} = \frac{y}{4} + \frac{- 4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 {(x - 2)}^{2}}{4} = \frac{y}{4} + \frac{- 4}{4}$

Divide ${(x - 2)}^{2}$ by $1$ .

${(x - 2)}^{2} = \frac{y}{4} + \frac{- 4}{4}$

Simplify the right side.

Divide $- 4$ by $4$ .

${(x - 2)}^{2} = \frac{y}{4} - 1$

Step 5

Factor.

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

${(x - 2)}^{2} = \frac{y}{4} - 1 \cdot \frac{4}{4}$

Combine $- 1$ and $\frac{4}{4}$ .

${(x - 2)}^{2} = \frac{y}{4} + \frac{- 1 \cdot 4}{4}$

Combine the numerators over the common denominator.

${(x - 2)}^{2} = \frac{y - 1 \cdot 4}{4}$

Multiply $- 1$ by $4$ .

${(x - 2)}^{2} = \frac{y - 4}{4}$

Reorder terms.

${(x - 2)}^{2} = \frac{1}{4} (y - 4)$